Find $ \lim_{x\to -3}g(x)$ for $g(x)=x^2-x-1$.
Answer: $g$ is a polynomial function. Polynomial functions are continuous across their entire domain, and their domain is all real numbers. In other words, for any polynomial $p$ and any possible input $c$, we know that this equality holds: $\lim_{x\to c}p(x)=p(c)$ Therefore, in order to find $ \lim_{x\to -3}g(x)$, we can simply evaluate $g$ at $x=-3$. $\begin{aligned} &\phantom{=}g(x) \\\\ &=x^2-x-1 \\\\ &=(-3)^2-(-3)-1 \gray{\text{Substitute }x=-3} \\\\ &=9+3-1 \\\\ &=11 \end{aligned}$ In conclusion, $ \lim_{x\to -3}g(x)=11$.